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 A230549 Coins left after packing twin hearts patterns into n X n coins. 6
 4, 5, 8, 13, 12, 21, 32, 33, 40, 57, 48, 69, 84, 85, 96, 125, 108, 141, 160, 161, 176, 217, 192, 237, 260, 261, 280, 333, 300, 357, 384, 385, 408, 473, 432, 501, 532, 533, 560, 637, 588, 669, 704, 705, 736, 825, 768, 861 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Twin hearts (6c4a type) is one of total 17 distinct patterns appearing in 3X2 coins where each pattern consists of 6 perimeter parts from each coin and forms a continuous area. a(n) is total coins left after packing twin hearts patterns (6c4a type: 6-curves cover 4 coins) into n X n coins with rotation not allowed. The total twin hearts patterns is A230548 and voids left is A230550. See illustration in links. LINKS Kival Ngaokrajang, Illustration of initial terms (U) FORMULA a(n) = n^2 - 4*A230548(n). G.f.: x^2 * (-3*x^10 - 4*x^8 + 3*x^7 + 8*x^6 + 4*x^5 - x^4 + 4*x^3 + 4*x^2 + 5*x + 4)/(1+x^3)*(1-x^3)^2*(1-x^2). (conjectured). - Ralf Stephan, Oct 30 2013 PROG (Small Basic) col = 1 row = 0 For n = 2 To 100   add = 0   If Math.Remainder(n, 2) * Math.Remainder(n, 3) <> 0 Then     add = 1   EndIf   If n >= 4 And Math.Remainder(n, 2) = 0 Then     col = col + 1   EndIf   If n >= 3 And Math.Remainder(n, 3) = 0 Then     row = row + 1   EndIf   U = n * n - (col * row + add)*4   TextWindow.Write(U+", ") EndFor CROSSREFS Cf. A008795, A230370 (3-curves); A074148, A227906, A229093, A229154 (4-curves); A001399, A230267, A230276 (5-curves); A229593, A228949, A229598, A002620 (6-curves). Sequence in context: A061765 A242274 A297419 * A133940 A174398 A030978 Adjacent sequences:  A230546 A230547 A230548 * A230550 A230551 A230552 KEYWORD nonn AUTHOR Kival Ngaokrajang, Oct 23 2013 STATUS approved

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Last modified July 15 04:34 EDT 2020. Contains 335763 sequences. (Running on oeis4.)